Question

Suppose the charge q2 can be moved left or right along a line connecting charges q1 and q3. Given that q = +15 µC, find the distance from q1 where q2 experiences a net electrostatic force of zero? (The charges q1 and q3 are separated by a fixed distance of 36 cm.)
q1=+q, q2=-2.0q, q3=+3.0q
magnitude in cm ?

direction?

Answer 1

F(q2) = ke*q1*q2/(r12)^2 + ke*q3*q2/(r23)^2 = 0

or

q1*q2/(r12)^2 = q3*q2/(r23)^2

q*-2q/(r12)^2 = 3q*-2q/(r23)^2

-2*q^2/(r12)^2 = -6q^2/(r23)^2

or

1/(r12)^2 = 3/(r23)^2

where r12 is the distance between charge 1 and 2; r23 is the distance bewteen charge 2 and 3. For symmetry sake, put q2 and zero. Then q2 must be between q1 and q3, and (r12)^2 is the same as r1^2, when r1 is the coordinate of q1; r23^2 is the same as r3^2, where r3 is the coordinate of q3.

you know that -r1 + r3 = 36, or r3 = 36 + r1. Substitute this into the above equation and solve for r1, the distance from q1 where q2 experiences a net electrostatic force of zero